[機統] 基本機率事件-台大電子所消失
In a contest , contestants A , B and C are asked , in turn , a question.
If a contestant gives a wrong answer to the question , he or she will be
dropped out of the game. the remaining two will continue to compete
until one of them drops out. The last person remaining is the winner.
Suppose that a contestant knows the answer to a question independently
of the other contestants , with probability P. Let ABC represent the
event that A drops first , B next , and C wins . Calculate the probability
of P{ABC)
解答 : (1-P)^2 + P^3(1-P)^2+P^6(1-P)^2+......
+(1-P)^2*P^2+P^3(1-P)^2*P^2+P^6(1-P)^2*P^2+.....
+(1-P)^2*P^4+P^3(1-P^2)*P^4+P^6(1-P^2)*P^4+.....
~
= (1-P)^2/(1-P^2)*(1/1-P^3)
想請問一下列式成上面是如何列的，謝謝!!
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